Question

Light of wavelength 'λ' is incident on a single slit of width 'a' and the distance between slit and screen is 'D'. In diffraction pattern, if slit width is equal to the width of the central maximum then 'D' is equal to ______.

Options

• `"a"/(2lambda)`

• `"a"^2/(2lambda)`

• `"a"/(lambda)`

• `"a"^2/(lambda)`

Answer 1

Light of wavelength 'λ' is incident on a single slit of width 'a' and the distance between slit and screen is 'D'. In diffraction pattern, if slit width is equal to the width of the central maximum then 'D' is equal to `underline("a"^2/(2lambda))`.

Explanation:

The diffraction pattern due to a single slit is shown below

The width of central maximum is given by

`2"y" = (2"D"lambda)/"a"`   ....(i)

where, λ = wavelength of incident light.

Here, a = 2y, then from Eq. (i}, we get

a = `(2"D"lambda)/"a"`

`=> "D" = "a"^2/(2lambda)`